I've had a 375/338 Taylor for years. An easy wildcat to do. Use 458WM brass and run into the die. A little faster than a 375H&H with less powder and on a standard length magnum action.
I built mine on a CZ (modern) Mauser action (had been trued), an Atinson/Marquart match barrel cut to 22" (I was going to go to 21") done to #2 contour. Timney trigger, Ruger rear sight, PMC banded front ramp, PMC barrel band and to save $$ used a B&C stock (painted flat black), pillar bedded. Had visions to someday go to Fajen wood but never did. Also used a 1.5x5 B&L.
As far as the shorter barrel...Only using medium burning powder (IMR4064), so don't need a long barrel. Because of this and the weight of the gun, recoil is (for example) a lot less than my 338WM or 300WM.
Shoots 270gr Hornady, 300gr Sierra, 300gr Partition realy well. I tried to get some lighter bullets to work, but results were not good.